第14卷第5期 智能系统学报 Vol.14 No.5 2019年9月 CAAI Transactions on Intelligent Systems Sept.2019 D0:10.11992/tis.201810021 网络出版地址：http:/kns.cnki.net/kcms/detail/23.1538.TP.20190527.1345.006html 因素表示的信息空间与广义概率逻辑 汪培庄，周红军2，何华灿3，钟义信4 (1.辽宁工程技术大学智能工程与数学研究院，辽宁阜新123000；2.陕西师范大学数学学院，陕西西安 710062:3.西北工业大学计算机学院.陕西西安710072：4.北京邮电大学智能科学技术中心，北京100876) 摘要：国内外近年来所提出的广义概率逻辑对于人工智能的发展有重要意义。能否反映变换演化的实际场 景，使逻辑判断能够灵活变通，这是广义概率逻辑发展的关键。为了解决这一问题，本文的目是以信息空间作 为逻辑与实际场景的接口。有了这个接口，逻辑判断就能反映变幻莫测的实际场景。本文的方法是用因素空 间来定义表现论域以形成新的信息空间，将谓词中的变元取为因素，在已有的逻辑系统中加上本文所提出的背 景公理，所有的推理都是在一定背景之下的推理，不同的背景会推出不同的结论。结果是新的逻辑既能维系 Stoe表示定理的表现要求，又能变得更加灵活有效。结论能使广义概率逻辑更有效地服务于人工智能。为了 配合机制主义人工智能的需要，本文还特别提出了语法-语用对接的方法和目标驱动的逆向推理设想.最后为 泛逻辑的3种连续算子对进行了数学证明。 关键词：机制主义人工智能；泛逻辑；计量概率逻辑；因素空间；模糊集；可能性空间；谓词演算；随机集落影 中图分类号：TP18文献标志码：A文章编号：1673-4785(2019)05-0843-10 中文引用格式：汪培庄，周红军，何华灿，等.因素表示的信息空间与广义概率逻辑.智能系统学报，2019,14（⑤）：843-852. 英文引用格式：VANG Peizhuang,ZHOU Hongjun,.HE Huacan,etal.Factorial information space and generalized probability lo- gic[J].CAAI transactions on intelligent systems,2019,14(5):843-852. Factorial information space and generalized probability logic WANG Peizhuang',ZHOU Hongjun',HE Huacan',ZHONG Yixin' (1.Institute of Intelligence Engineering and Math,Liaoning Technical University,Fuxin 123000,China;2.College of Mathematics,Shannxi Normal University,Xi'an 710062,China;3.School of Computer Science,Northwestern Poly- technical University,Xi'an 710072,China;4.Center for Intelligent Science and Technology,Beijing University of Posts Telecommunications,Beijing 100876,China) Abstract:The generalized probabilistic logic proposed in recent years is of great significance to the development of arti- ficial intelligence.Make flexible judgment that reflects the scene of actual transformation and evolution is the key to the development of the generalized probability logic.Considering this,this paper takes the information space as the inter- face between logic and actual scene.With this interface,logical judgment can reflect unpredictable real situations.The method in this paper is to use factors space to define the representation domain to form the information space.Then pre- dicate variables are taken as factors,and background axioms are added into the existing logic system.Reasoning is taken under a certain background,different backgrounds will derive different conclusions.The result is that the new logic can not only maintain the rational requirement of the Stone representation theorem but can also make decisions more flex- ibly and effectively.The conclusion is that the generalized probabilistic logic can serve artificial intelligence more ef- fectively.To meet the need of mechanistic artificial intelligence,this paper proposes the grammar-pragmatic docking method and the goal-driven backward reasoning.Finally,a mathematical proof is given for three couples of continuous operators in universal logic. Keywords:mechanism based artificial intelligence;universal logic;econometric probability logic;factors space;fuzzy sets;possibility space;predicate calculus,random falling shadow 收稿日期：2018-10-17.网络出版日期：2019-05-28. 机制主义的人工智能理论抓住并提升了目前 基金项目：国家自然科学基金(61350003.60273087.60873001). 通信作者：汪培庄.E-mail:peizhuangw@126.com. 三大流派的共性，为人工智能理论的发展构建了DOI: 10.11992/tis.201810021 网络出版地址: http://kns.cnki.net/kcms/detail/23.1538.TP.20190527.1345.006.html 因素表示的信息空间与广义概率逻辑 汪培庄1，周红军2，何华灿3，钟义信4 （1. 辽宁工程技术大学 智能工程与数学研究院，辽宁 阜新 123000; 2. 陕西师范大学 数学学院，陕西 西安 710062; 3. 西北工业大学 计算机学院，陕西 西安 710072; 4. 北京邮电大学 智能科学技术中心，北京 100876） 摘 要：国内外近年来所提出的广义概率逻辑对于人工智能的发展有重要意义。能否反映变换演化的实际场 景，使逻辑判断能够灵活变通，这是广义概率逻辑发展的关键。为了解决这一问题，本文的目是以信息空间作 为逻辑与实际场景的接口。有了这个接口，逻辑判断就能反映变幻莫测的实际场景。本文的方法是用因素空 间来定义表现论域以形成新的信息空间，将谓词中的变元取为因素，在已有的逻辑系统中加上本文所提出的背 景公理，所有的推理都是在一定背景之下的推理，不同的背景会推出不同的结论。结果是新的逻辑既能维系 Stone 表示定理的表现要求，又能变得更加灵活有效。结论能使广义概率逻辑更有效地服务于人工智能。为了 配合机制主义人工智能的需要，本文还特别提出了语法-语用对接的方法和目标驱动的逆向推理设想，最后为 泛逻辑的 3 种连续算子对进行了数学证明。 关键词：机制主义人工智能；泛逻辑；计量概率逻辑；因素空间；模糊集；可能性空间；谓词演算；随机集落影 中图分类号：TP18 文献标志码：A 文章编号：1673−4785(2019)05−0843−10 中文引用格式：汪培庄, 周红军, 何华灿, 等. 因素表示的信息空间与广义概率逻辑 [J]. 智能系统学报, 2019, 14(5): 843–852. 英文引用格式：WANG Peizhuang, ZHOU Hongjun, HE Huacan, et al. Factorial information space and generalized probability lo￾gic[J]. CAAI transactions on intelligent systems, 2019, 14(5): 843–852. Factorial information space and generalized probability logic WANG Peizhuang1 ，ZHOU Hongjun2 ，HE Huacan3 ，ZHONG Yixin4 (1. Institute of Intelligence Engineering and Math, Liaoning Technical University, Fuxin 123000, China; 2. College of Mathematics, Shannxi Normal University, Xi’an 710062, China; 3. School of Computer Science, Northwestern Poly￾technical University, Xi’an 710072, China; 4. Center for Intelligent Science and Technology, Beijing University of Posts Telecommunications, Beijing 100876, China) Abstract: The generalized probabilistic logic proposed in recent years is of great significance to the development of arti￾ficial intelligence. Make flexible judgment that reflects the scene of actual transformation and evolution is the key to the development of the generalized probability logic. Considering this, this paper takes the information space as the inter￾face between logic and actual scene. With this interface, logical judgment can reflect unpredictable real situations. The method in this paper is to use factors space to define the representation domain to form the information space. Then pre￾dicate variables are taken as factors, and background axioms are added into the existing logic system. Reasoning is taken under a certain background, different backgrounds will derive different conclusions. The result is that the new logic can not only maintain the rational requirement of the Stone representation theorem but can also make decisions more flex￾ibly and effectively. The conclusion is that the generalized probabilistic logic can serve artificial intelligence more ef￾fectively. To meet the need of mechanistic artificial intelligence, this paper proposes the grammar-pragmatic docking method and the goal-driven backward reasoning. Finally, a mathematical proof is given for three couples of continuous operators in universal logic. Keywords: mechanism based artificial intelligence; universal logic; econometric probability logic; factors space; fuzzy sets; possibility space; predicate calculus; random falling shadow 机制主义的人工智能理论抓住并提升了目前 三大流派的共性，为人工智能理论的发展构建了 收稿日期：2018−10−17. 网络出版日期：2019−05−28. 基金项目：国家自然科学基金 (61350003，60273087，60873001). 通信作者：汪培庄. E-mail: peizhuangw@126.com. 第 14 卷第 5 期 智 能 系 统 学 报 Vol.14 No.5 2019 年 9 月 CAAI Transactions on Intelligent Systems Sept. 2019